Big Flip Graphs and Their Automorphism Groups
Geometric Topology
2022-01-28 v1
Abstract
In this paper, we study the relationship between the mapping class group of an infinite-type surface and the simultaneous flip graph, a variant of the flip graph for infinite-type surfaces defined by Fossas and Parlier. We show that the extended mapping class group is isomorphic to a proper subgroup of the automorphism group of the flip graph, unlike in the finite-type case. This shows that Ivanov's metaconjecture, which states that any "sufficiently rich" object associated to a finite-type surface has the extended mapping class group as its automorphism group, does not extend to simultaneous flip graphs of infinite-type surfaces.
Cite
@article{arxiv.2201.11272,
title = {Big Flip Graphs and Their Automorphism Groups},
author = {Assaf Bar-Natan and Advay Goel and Brendan Halstead and Paul Hamrick and Sumedh Shenoy and Rishi Verma},
journal= {arXiv preprint arXiv:2201.11272},
year = {2022}
}
Comments
8 pages, 3 figures